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Diophantine equation in integers with odd digits

Source: VII Caucasus Mathematical Olympiad

March 13, 2022
combinatorics

Problem Statement

Let SS be the set of all 565^6 positive integers, whose decimal representation consists of exactly 6 odd digits. Find the number of solutions (x,y,z)(x,y,z) of the equation x+y=10zx+y=10z, where x∈Sx\in S, y∈Sy\in S, z∈Sz\in S.
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